A particle at the end of a spring executes simple harmonic motion with a period $$t1$$, while the corresponding period for another spring is $$t2$$. If the period of oscillation with the two springs in series is T, then

Question

A particle at the end of a spring executes simple harmonic motion with a period $$t1$$, while the corresponding period for another spring is $$t2$$. If the period of oscillation with the two springs in series is T, then

Infinity Learn · Accepted Answer

$$t1$$ $$=$$ $$2$$$$π$$$$mk1$$    and $$t2$$ $$=$$ $$2$$$$π$$$$mk2In$$ series, effective spring constant, k $$=$$ $$k1k2k1+k2$$∴  Time period, T $$=$$ $$2$$$$π$$$$m(k1+k2)k1k2----------(i)Now$$, $$t12+t22$$ $$=$$ $$4$$$$π$$$$2m(1k1+1k2)$$ $$=$$ $$4$$$$π$$$$2m(k1+k2)k1k2$$             $$t12+t22$$ $$=$$ $$T2$$.            [Using equation (ii)]

A particle at the end of a spring executes simple harmonic motion with a period $t_{1}$ , while the corresponding period for another spring is $t_{2}$ . If the period of oscillation with the two springs in series is T, then

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A particle at the end of a spring executes simple harmonic motion with a period t1, while the corresponding period for another spring is t2. If the period of oscillation with the two springs in series is T, then

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A particle at the end of a spring executes simple harmonic motion with a period $t_{1}$ , while the corresponding period for another spring is $t_{2}$ . If the period of oscillation with the two springs in series is T, then